1 / 85

Advanced Algebra Chapter 13

Advanced Algebra Chapter 13. Trigonometric Ratios and FUN ctions. Right Triangle Trigonometry—13.1. Getting Started. The Greek Alphabet!. Getting Started. Right Triangles Sides Hypotenuse Adjacent Opposite Angles Right Angle Theta Other angle

quana
Download Presentation

Advanced Algebra Chapter 13

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Advanced Algebra Chapter 13 Trigonometric Ratios and FUNctions

  2. Right Triangle Trigonometry—13.1

  3. Getting Started The Greek Alphabet!

  4. Getting Started • Right Triangles • Sides • Hypotenuse • Adjacent • Opposite • Angles • Right Angle • Theta • Other angle • The sum of all angles in any triangle is:

  5. Getting Started • What else do we know about right triangles? • There was a guy with a theorem!

  6. Trig • Six Trig functions • Sine • Cosine • Tangent • Cotangent • Cosecant • Secant

  7. Trig FUNctions

  8. Soh Cah Toa

  9. Trig FUNctions

  10. Evaluate all six trigonometric FUNctions for the given triangle

  11. Evaluate all six trigonometric FUNctions for the given triangle

  12. Evaluate all six trigonometric functions for the given triangle

  13. Angles of Elevation or Depression • Elevation • Looking Up • Depression • Looking Down

  14. Angles A support cable from a radio tower makes an angle of 56 degrees with the ground. If the cable is 250 feet long, how far above the ground does it meet the tower?

  15. Angles An airplane flying at 20,000 feet is headed toward an airport. The landing systems sends radar signals from the runway to the airplane, recording a 5 degree angle of elevation. About how many miles is the airplane from the runway?

  16. p.772#15-40

  17. General Angles and Radian Measure—13.2

  18. Define: • Angle • Formed by two rays sharing a common endpoint known as the vertex

  19. Standard Position Standard Position Initial Side Terminal Side Positive v. Negative

  20. Angles 210 degrees

  21. Angles -45 degrees

  22. Angles 30 degrees -330 degrees 390 degrees Coterminal Angles

  23. Finding Coterminal Angles Two angles are coterminal iff one angle can be found my adding or subtracting multiples of 360 degrees

  24. Coterminal Angles Find 2 positive and 2 negative angles coterminal to the following: 70 degrees 115 degrees -5 degrees

  25. Circles What if we think about distance around a circle as a total of it’s angles? Circumference of a circle: So,

  26. Circles

  27. The Unit Circle

  28. Converting from one to another… 1 Radian is how many degrees: Rewriting Degrees as Radians: Rewriting Radians as Degrees

  29. Converting Convert 110 degrees to radians

  30. Converting Convert radians to degrees

  31. Why Radians? • Work great with circles • Already in terms of circumference so finding arc length is easy • What’s arc length? • Arc length (s) is the distance around a portion of a circle called a sector • What’s a sector? • Is a region of a circle bounded by two radii and the arc of the circle • The angle formed is called the central angle

  32. Arc Length and Area of a Sector

  33. p.780#28-58 Every 3rd

  34. Trig FUNctions of Any Angle—13.3

  35. Consider our Unit Circle again… Make a list of all of the x- and y-values What do you notice about these? What about pos/neg? We’ll come back to this…

  36. Consider our Unit Circle again… Could we find a short cut to this stuff? In other words, do we need the entire circle?

  37. Consider our Unit Circle again… • Everything we need happens in the 1st quadrant! • So, we use reference angles • Reference angle • Acute angle formed by the terminal side of the angle and the x-axis • i.e. use the shortest distance to the x-axis as your reference angle

  38. Find the reference angles for:

  39. Why reference angles and ordered pairs? • When on the unit circle: • Y-values: Sine values! • X-values: Cosine values!

  40. Define trig functions as:

  41. Signs of Trig Functions

  42. Signs of Trig Functions All Students Take Calculus Sine All Tells us which values are positive Tangent Cosine

  43. Using reference angles… • Find the sin of the following:

  44. Using reference angles • Find cos of the following?

  45. Using reference angles, • Find tan of the following:

  46. p.788#34-36, 38-60 Even

  47. Inverse Trig FUNctions—13.4

  48. Domain and Range • Domain • The numbers you plug IN to a function • Range • The numbers you get OUT of a function

  49. Inverse FUNctions • To get an inverse, we switch the domains and ranges! • For our new function • The old range becomes our new domain • The old domain becomes our new range

  50. Inverse FUNctions • Consider the sine function: • Domain • Range • How about inverse sine or • Domain • Range

More Related